Abstract
Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategies are required for an efficient application to problems of dimension ≥ 3. Recently, a stabilized multi-scale finite element method has been effectively applied to the Fokker-Planck equation effectively by means of a considerably reduction of the required number of elements. Also, the alternating directions implicit method shows good performance in terms of efficiency and accuracy. In this paper various finite difference and finite element methods are discussed and the results are compared using various numerical examples.
| Original language | English (US) |
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| State | Published - 2011 |
| Event | 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2011 - Corfu, Greece Duration: May 25 2011 → May 28 2011 |
Other
| Other | 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2011 |
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| Country/Territory | Greece |
| City | Corfu |
| Period | 5/25/11 → 5/28/11 |
Keywords
- Duffing oscillator
- Finite difference method
- Finite element method
- Fokker-planck equation
- Linear oscillator
- Multi- scale finite element method
ASJC Scopus subject areas
- Computers in Earth Sciences
- Geotechnical Engineering and Engineering Geology
- Computational Mathematics